The Fixed - Point Theorems of

Sibylla Priess-Crampe and Paulo Ribenboim recently established a general xed-point theorem for multivalued mappings deened on generalized ultrametric spaces, and introduced it to the area of logic programming semantics. We discuss, in this context, the applications which have been made so far of this theorem and of its corollaries. In particular, we will relate these results to Scott-Ershov domains, familiar in programming language semantics, and to the generalized metrics of Khamsi, Kreinovich and Misane which have been applied, by these latter authors, to logic programming. Amongst other things, we will also show that a uniied treatment of the xed-point theory of wide classes of programs can be given by means of the theorems of Priess-Crampe and Ribenboim.